Subgroups — C₃×C₄×Dic₅ #6679

Order 240.

60 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₃×C₄×C₅	C₂	1	1	yes	maximal, characteristic
2	C₂×C₃×Dic₅	C₂	1	2	yes	maximal
3	C₄×Dic₅	C₃	1	1	yes	maximal, characteristic, direct product factor, Hall
4	C₂²×C₃×C₅	C₂²	1	1	yes	characteristic
5	C₃×C₄×C₅	C₄	1	2	yes	complemented
6	C₃×Dic₅	C₄	1	4	yes	direct product factor
7	C₃×C₄²	—	5	1	no	maximal, Hall
8	C₂×C₄×C₅	C₂×C₃	1	1	yes	characteristic
9	C₂×Dic₅	C₂×C₃	1	2	yes	—
10	C₂×C₃×C₅	C₂×C₄	1	2	yes	—
11	C₂×C₃×C₅	C₂×C₄	1	1	yes	characteristic
12	C₂×C₃×C₄	—	5	2	no	—
13	C₂×C₃×C₄	D₅	1	1	yes	characteristic
14	C₂²×C₅	C₂²×C₃	1	1	yes	characteristic
15	C₄×C₅	C₃×C₄	1	2	yes	complemented
16	Dic₅	C₃×C₄	1	4	yes	direct product factor
17	C₄²	—	5	1	no	Sylow
18	C₃×C₅	C₄²	1	1	yes	characteristic, complemented, Hall
19	C₂²×C₃	C₂×D₅	1	1	yes	characteristic
20	C₃×C₄	—	5	4	no	—
21	C₃×C₄	Dic₅	1	2	yes	direct product factor
22	C₂×C₅	C₂×C₃×C₄	1	2	yes	—
23	C₂×C₅	C₂×C₃×C₄	1	1	yes	characteristic
24	C₂×C₄	—	5	2	no	—
25	C₂×C₄	C₃×D₅	1	1	yes	characteristic
26	C₂×C₃	C₄×D₅	1	2	yes	—
27	C₂×C₃	C₂×Dic₅	1	1	yes	characteristic
28	C₅	C₃×C₄²	1	1	yes	characteristic, complemented, Sylow
29	C₂²	C₂×C₃×D₅	1	1	yes	characteristic
30	C₄	—	5	4	no	—
31	C₄	C₃×Dic₅	1	2	yes	direct product factor
32	C₃	C₄×Dic₅	1	1	yes	characteristic, direct product factor, Sylow
33	C₂	C₃×C₄×D₅	1	2	yes	—
34	C₂	C₂×C₃×Dic₅	1	1	yes	characteristic

Splittings G = N ⋊ H with N normal; H ≅ G/N.

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.